What Brand & Model is the fridge?
Typically they are 2 way (AC & LP).........some are 3 way (AC, LP & DC)
Those are the types of heating soures
AC is used when 110V power is available
LP is used when NO 110V power
DC is used when traveling and battery draw can be replaced via alternator etc.
If you have an 'auto' setting on fridge upper panel just place it in auto.
When you have 110V AC power it will run on that source. When you drop AC power source fridge will automatically change to LP operation.
Inverter takes DC power from battery converts it to 110V AC power source and can be used to operate some AC appliances BUT you are limited on what appliances you can run plus you need a means of recharging them